An instructor gives his class a set of 13 problems with the information that the next quiz will consist of a random selection of 5 of them.

Question

An instructor gives his class a set of 13 problems with the information that the next quiz will consist of a random selection of 5 of them. If a student has figured out how to do 11 of the problems, what is the probability the he or she will answer all 5 problems correctly? At least 4 problems correctly?

Answer 1

Imagine your making the list of the 5 problems. For the first one, there is a 11/13 chance that it will be one that has already been solved. For the next problem on the list, there are 10 solved problems out of a possible 12. Continue in this pattern for all five to get

 

(11/13)(10/12)(9/11)(8/10)(7/9) = 56/156 = 36%

 

If it's just four, then the answer is

 

(11/13)(10/12)(9/11)(8/10) = 72/156 = 46%